{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YZXGYX2XR7BTY3OEZWVTBVEG5C","short_pith_number":"pith:YZXGYX2X","canonical_record":{"source":{"id":"1105.3424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-05-17T16:13:04Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"f1d74b46fb54cb13a5a438e1d8167b2b3f961d9bbeb22176595f9db83068336e","abstract_canon_sha256":"26bd0cc6c2c24b24d966761331a3104635f6f3b8f281b65c5917de86f7f9ed17"},"schema_version":"1.0"},"canonical_sha256":"c66e6c5f578fc33c6dc4cdab30d486e8a5e0329bee5ad9e20c7b174548c79ef9","source":{"kind":"arxiv","id":"1105.3424","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3424","created_at":"2026-05-18T02:21:59Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3424v1","created_at":"2026-05-18T02:21:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3424","created_at":"2026-05-18T02:21:59Z"},{"alias_kind":"pith_short_12","alias_value":"YZXGYX2XR7BT","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YZXGYX2XR7BTY3OE","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YZXGYX2X","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YZXGYX2XR7BTY3OEZWVTBVEG5C","target":"record","payload":{"canonical_record":{"source":{"id":"1105.3424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-05-17T16:13:04Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"f1d74b46fb54cb13a5a438e1d8167b2b3f961d9bbeb22176595f9db83068336e","abstract_canon_sha256":"26bd0cc6c2c24b24d966761331a3104635f6f3b8f281b65c5917de86f7f9ed17"},"schema_version":"1.0"},"canonical_sha256":"c66e6c5f578fc33c6dc4cdab30d486e8a5e0329bee5ad9e20c7b174548c79ef9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:59.687993Z","signature_b64":"gOWordZM+K2fJZlpdQ/kKjbgLP8dqlpV3DbGrbHes96lvnoVl9AZdmapc1MXN/U0FeOYrOcoLMHEm+sMJ3OxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c66e6c5f578fc33c6dc4cdab30d486e8a5e0329bee5ad9e20c7b174548c79ef9","last_reissued_at":"2026-05-18T02:21:59.687099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:59.687099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.3424","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:21:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bmhlkAv5eKA0VPnxs759d7+XyDFFiUUXtOboPOdHIB62fh/T5oAUJ7Xa52tPDJNMRxgBSk34Y9z2kYRAVxsSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:44:38.365703Z"},"content_sha256":"f525193673a0fe022c18c40e7886ba1a80bc0269284f1c34f7472ac1855cbfb4","schema_version":"1.0","event_id":"sha256:f525193673a0fe022c18c40e7886ba1a80bc0269284f1c34f7472ac1855cbfb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YZXGYX2XR7BTY3OEZWVTBVEG5C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Competing epidemics on complex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Brian Karrer, M. E. J. Newman","submitted_at":"2011-05-17T16:13:04Z","abstract_excerpt":"Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same network at the same time, where infection with either disease gives an individual subsequent immunity to both. Using a combination of analytic and numerical methods, we derive the phase diagram of the system and estimates of the expected final numbers of individuals infected with each disease. The system shows an unusual dynamical transition between dominance "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3424","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:21:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZHCz4tEnEy7DU+wHuKa31qo5J6NHqjN1SpYW85AMx3PlCbGyxGcmxwtohhTUBU+u2KDj3s0X4YTX5FKJBsdJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:44:38.366052Z"},"content_sha256":"05e0d37d3bd52fe0a48de840b370895758e4e9ef70aa1bc5f5adee879529d985","schema_version":"1.0","event_id":"sha256:05e0d37d3bd52fe0a48de840b370895758e4e9ef70aa1bc5f5adee879529d985"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZXGYX2XR7BTY3OEZWVTBVEG5C/bundle.json","state_url":"https://pith.science/pith/YZXGYX2XR7BTY3OEZWVTBVEG5C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZXGYX2XR7BTY3OEZWVTBVEG5C/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T18:44:38Z","links":{"resolver":"https://pith.science/pith/YZXGYX2XR7BTY3OEZWVTBVEG5C","bundle":"https://pith.science/pith/YZXGYX2XR7BTY3OEZWVTBVEG5C/bundle.json","state":"https://pith.science/pith/YZXGYX2XR7BTY3OEZWVTBVEG5C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZXGYX2XR7BTY3OEZWVTBVEG5C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YZXGYX2XR7BTY3OEZWVTBVEG5C","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"26bd0cc6c2c24b24d966761331a3104635f6f3b8f281b65c5917de86f7f9ed17","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-05-17T16:13:04Z","title_canon_sha256":"f1d74b46fb54cb13a5a438e1d8167b2b3f961d9bbeb22176595f9db83068336e"},"schema_version":"1.0","source":{"id":"1105.3424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3424","created_at":"2026-05-18T02:21:59Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3424v1","created_at":"2026-05-18T02:21:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3424","created_at":"2026-05-18T02:21:59Z"},{"alias_kind":"pith_short_12","alias_value":"YZXGYX2XR7BT","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YZXGYX2XR7BTY3OE","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YZXGYX2X","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:05e0d37d3bd52fe0a48de840b370895758e4e9ef70aa1bc5f5adee879529d985","target":"graph","created_at":"2026-05-18T02:21:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same network at the same time, where infection with either disease gives an individual subsequent immunity to both. Using a combination of analytic and numerical methods, we derive the phase diagram of the system and estimates of the expected final numbers of individuals infected with each disease. The system shows an unusual dynamical transition between dominance ","authors_text":"Brian Karrer, M. E. J. Newman","cross_cats":["cond-mat.stat-mech","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-05-17T16:13:04Z","title":"Competing epidemics on complex networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3424","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f525193673a0fe022c18c40e7886ba1a80bc0269284f1c34f7472ac1855cbfb4","target":"record","created_at":"2026-05-18T02:21:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"26bd0cc6c2c24b24d966761331a3104635f6f3b8f281b65c5917de86f7f9ed17","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-05-17T16:13:04Z","title_canon_sha256":"f1d74b46fb54cb13a5a438e1d8167b2b3f961d9bbeb22176595f9db83068336e"},"schema_version":"1.0","source":{"id":"1105.3424","kind":"arxiv","version":1}},"canonical_sha256":"c66e6c5f578fc33c6dc4cdab30d486e8a5e0329bee5ad9e20c7b174548c79ef9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c66e6c5f578fc33c6dc4cdab30d486e8a5e0329bee5ad9e20c7b174548c79ef9","first_computed_at":"2026-05-18T02:21:59.687099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:59.687099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gOWordZM+K2fJZlpdQ/kKjbgLP8dqlpV3DbGrbHes96lvnoVl9AZdmapc1MXN/U0FeOYrOcoLMHEm+sMJ3OxBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:59.687993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f525193673a0fe022c18c40e7886ba1a80bc0269284f1c34f7472ac1855cbfb4","sha256:05e0d37d3bd52fe0a48de840b370895758e4e9ef70aa1bc5f5adee879529d985"],"state_sha256":"d328d8ce34d34450e1252981ea5406b100f093da6a3e2467759e8581cac31937"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q4bJNlK4eTDNhFdfTTc+5TXSWCBhVlj4yIfmx5AdXeY+1nDxIQsaETrvGF5Z3UiKWdOdy01HnSQo2rTj2EGBCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:44:38.368022Z","bundle_sha256":"609f78fd4b976128855b6824e9663f1f217e98a92917d08890e838deb976a8f2"}}